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Equivalence and orthogonality of Gaussian measures on spheres

Lookup NU author(s): Professor Emilio Porcu

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Abstract

© 2018 Elsevier Inc. The equivalence of Gaussian measures is a fundamental tool to establish the asymptotic properties of both prediction and estimation of Gaussian fields under fixed domain asymptotics. The paper solves Problem 18 in the list of open problems proposed by Gneiting (2013). Specifically, necessary and sufficient conditions are given for the equivalence of Gaussian measures associated to random fields defined on the d-dimensional sphere Sd, and with covariance functions depending on the great circle distance. We also focus on a comparison of our result with existing results on the equivalence of Gaussian measures for isotropic Gaussian fields on Rd+1 restricted to the sphere Sd. For such a case, the covariance function depends on the chordal distance being an approximation of the true distance between two points located on the sphere. Finally, we provide equivalence conditions for some parametric families of covariance functions depending on the great circle distance. An important implication of our results is that all the parameters indexing some families of covariance functions on spheres can be consistently estimated. A simulation study illustrates our findings in terms of implications on the consistency of the maximum likelihood estimator under fixed domain asymptotics.


Publication metadata

Author(s): Arafat A, Porcu E, Bevilacqua M, Mateu J

Publication type: Article

Publication status: Published

Journal: Journal of Multivariate Analysis

Year: 2018

Volume: 167

Pages: 306-318

Print publication date: 01/09/2018

Online publication date: 20/05/2018

Acceptance date: 02/04/2018

ISSN (print): 0047-259X

ISSN (electronic): 1095-7243

Publisher: Academic Press Inc.

URL: https://doi.org/10.1016/j.jmva.2018.05.005

DOI: 10.1016/j.jmva.2018.05.005


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